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mathmath333
 one year ago
functions
mathmath333
 one year ago
functions

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} &\normalsize \text{Find the maximim value of the function}\hspace{.33em}\\~\\ & \dfrac{1}{x^23x+2} \hspace{.33em}\\~\\ \end{align}}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2interval given ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2with out interval this maximum value diverges to infinity.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0this question means that i have to minimize \(\large \color{black}{\begin{align} x^23x+2 \hspace{.33em}\\~\\ \end{align}}\) right ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2should be, or els... i mean there is not maximum value here, if you are taking over \((\infty,~+\infty)\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.21/that ? or, just that ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0lol its \(\large \color{black}{\begin{align} \dfrac{1}{x^23x+2} \hspace{.33em}\\~\\ \end{align}}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2\(\large\color{black}{ \displaystyle f(x)=\frac{1}{x^23x+2} }\) and you want to find absolute minimum, right?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2well, I can tell you that the limit as x approaches \(\pm\)infinity is going to be 0.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2we can plot, I am guessing it is something like dw:1435010239497:dw

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0i want to find the maximum value of this \(\large \color{black}{\begin{align} \dfrac{1}{x^23x+2} \hspace{.33em}\\~\\ \end{align}}\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0how i prove that with algebra

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2even the minimum doesn't exist.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2with algebra, even with no calc ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2\(\large\color{black}{ \displaystyle f(x)=\frac{1}{x^23x+2} }\) it has vertical asymptotes, can you find them for me?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} x=2,\ 1 \hspace{.33em}\\~\\ \end{align}}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2and, the best thing I can see here is to use the idea of a limit to see where range tends to the close we get to x=1 and x=2. I don't really know a purely algebraic proof for why this function has no max or min.

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0that has a max actually

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2https://www.desmos.com/calculator keep scrollin up

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2on a certain interval, no doubt (unless it has a domain gap)

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0i think it attains one max does not perhaps required any domain to get it or i think

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0your graph does not show up see here https://www.desmos.com/calculator

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2i don't think there is a max. that is due to an asymptote  two of them, there.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2we can find the limit from the right and from the left as x approaches 1 and 2.

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0http://prntscr.com/7k4q1l here see that bottom part of the graph

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0with calculus we can prove it has a max value but @mathmath333 is looking for a different way

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2this graph goes further down and up if you scroll on desmos, but we can go ahead and take any limit that is closed from either side of any of the asymptotes you wish to choose.....

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0i mean here local max not abolute of course

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0how to find that local max

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2oh, but the question is asking for absolute doesn't it?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2that is what i would think of course

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0first let's write that as 1/(x1)(x2)

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0i had thought of absolute too, just not sure about it!

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0yes the question is asking absolute, i just asked that of curiosity

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2this function is pretty weird. I wonder what would it model

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2i mean in real world

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0you want to then prove there is no max algebraically

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2would that include using ideas from calc but not its techniques?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2I am stubborn on the idea of a limit. A limit would simply show that as it approaches __ it can be infinitely large/small

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0ok i will try to bear with calculus

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2\(\large\color{black}{ \displaystyle \frac{1 }{x^23x+2} }\) we need to do only 1 asymptote for this

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2\(\large\color{black}{ \displaystyle \frac{1 }{x^23x+2} }\) lets plug in values that are less than, but close to 1

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2\(\large\color{black}{ \displaystyle f(0.9)=? }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2try plugging it yourself for close values to 1

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2these values are called approaching "from the left" because they are a buit less than 1

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2now, try to do f(1.5) f(1.1) f(1.01) f(1.001) and you will see where it goes "from the right"  for values that are greater than 1

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0suppose there exist a max max(1/(x^23x+2)=c 1/x^23x+2<c x^23x+2>1/c=l x^23x+2l>0

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0just some random stuff lol

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0coming back..

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0ok i need to go please comment if u found something

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0let's first consider the domain \(D_f: \{ x\in \mathbb{R}: x\ne1, x\ne 2 \}\)

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0that is (oo, 1)u(1, 2)u(2,oo)

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0we look at the sign of y when x<1 if y does not change the sign in that interval then i must not have a max seems that 1/(x2)(x1)>0 for x<1 same reasoning for x>2 ===> y>0 so only btw 1 and 2 left

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.0from the graph we knew for 1<x<2, y<4 we need to show this
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